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Cholesky Decomposition

N.H.F. Beebe and J. Linderberg, Simplifications in the generation and transformation of two‐electron integrals in molecular calculations, Int. J. Quant. Chem. 12, 683-705 (1977)

first serious realization (also implemented in CFOUR within the MINT integral package)
H. Koch, A.S. de Merás, T.B. Pedersen, Reduced scaling in electronic structure calculations using Cholesky decompositions, J. Chem. Phys. 118, 9481-9484 (2003)

efficient realization
S.D. Folkestad, E.F. Kjønstad, H. Koch, An efficient algorithm for Cholesky decomposition of electron repulsion integrals, J. Chem. Phys. 150, 194112 (2019)

realization with coupled-cluster and equation-of-motion coupled-cluster theory
E. Epifanovsky, D. Zuev, X. Feng, K. Khistayev, Y. Shao, A.I. Krylov, General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and qquation-of-motion methods: Theory and benchmarks, J. Chem. Phys. 139, 134105 (2013)

implementation in CFOUR with quadratically convergent SCF
T. Nottoli, J. Gauss, F. Lipparini, A black-box, general purpose quadratic self-consistent field code with and without Cholesky decomposition of the two-electron integrals, Mol. Phys. 119, e1974590 (2021)

implementation in CFOUR with CASSCF
T. Nottoli, J. Gauss, F. Lipparini, Second-order CASSCF algorithm with the Cholesky decomposition of the two-electron integrals, J. Chem. Theor. Comp. 17, 6819-6831 (2021)

geometrical gradients with Cholesky decomposition
X. Feng, E. Epifanovsky, J. Gauss, A.I. Krylov, Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks, J. Chem. Phys. 151, 014110 (2019)

NMR chemical shifts with Cholesky decomposition (CD-GIAO-MP2)
S. Burger, F. Lipparini, J. Gauss, S. Stopkowicz, NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals, J. Chem. Phys. 155, 074105 (2021)

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CFOUR is partially supported by the U.S. National Science Foundation.